The incompleted expression.

Algebra Level 4

$x^3 + y^3 + z^3 = nx^2y^2z^2$ Find the sum of all possible value of $$n \in \mathbb N^*$$ so that the expression above has at least one possible solution of $$x$$; $$y$$; $$z$$ $$\in \mathbb N^*$$.

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